Finite Group Databasebeta

← C11×#23916 #14601109

Subgroups — C11×#23916 #14601109

Order 2816.

1694 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3487C211yesmaximal, characteristic
2C2×C11×#536C211yesmaximal, characteristic, complemented
3C2×C11×#456C212yesmaximal, complemented
4C11×#3004C212yesmaximal, complemented
5C11×#2004C214yesmaximal, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1886C212yesmaximal, complemented
8C11×#1785C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×#137C2214yes—
13C11×#550—24no—
14C11×#548—24no—
15C11×#536—28no—
16C11×#535—22no—
17C11×#535C2212yes—
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×#124C2212yes—
20C11×#525—22no—
21C11×#525C2212yes—
22C2×C11×#123—22no—
23C2×C11×C22⋊Q8—22no—
24C11×#519C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#456—28no—
27C11×#451—24no—
28C11×#448—24no—
29C2×C11×#104C2214yes—
30C11×#419C2214yes—
31C2×C11×#101C2212yes—
32C2×C11×#100C2212yes—
33C11×#407C2212yes—
34C11×#339C2214yes—
35C11×2−1+4—24no—
36C11×2−1+4—42no—
37C2×C11×#41—24no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—24no—
41C2×C11×#41—42no—
42C2×C11×#41C2312yes—
43C22×Q8×C11—24no—
44C22×Q8×C11—22no—
45C22×Q8×C11—21no—
46C22×Q8×C11—24no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2312yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11D412yes—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D412yes—
54C23×C4×C11C2311yescharacteristic
55C11×#137—28no—
56C11×#137—44no—
57C2×C11×Q16—24no—
58C2×C11×SD16—24no—
59C2×C11×M16C2314yes—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8D418yescomplemented
62C11×#127—24no—
63C11×#127—22no—
64C11×#124—24no—
65C11×#124—24no—
66C11×#124—22no—
67C11×#124—24no—
68C11×#123—216no—
69C11×#123—22no—
70C11×C22⋊Q8—216no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8D414yes—
73C11×#121—24no—
74C11×#121—28no—
75C11×#121—24no—
76C11×#121D414yes—
77C11×#120—24no—
78C11×#120—22no—
79C4×Q8×C11—24no—
80C4×D4×C11—28no—
81C4×D4×C11—24no—
82C11×#117—22no—
83C11×#117—24no—
84C11×#117C2312yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11C2312yes—
90C11×#104—28no—
91C11×#103—28no—
92C11×#101—24no—
93C11×#100—42no—
94C11×C22⋊C8—24no—
95#23916C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11C2×D412yes—
97C24×C11C2×D411yescharacteristic
98C11×#41—24no—
99C11×#41—24no—
100C11×#41—416no—
101C11×#41—44no—
102C11×#41—48no—
103C11×#41—44no—
104C2×Q8×C11—24no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—24no—
110C2×Q8×C11—24no—
111C2×Q8×C11—416no—
112C2×Q8×C11—42no—
113C2×Q8×C11—48no—
114C2×Q8×C11—42no—
115C2×Q8×C11C2×D412yes—
116C2×Q8×C11C2×D414yes—
117C2×Q8×C11C2×D414yes—
118C2×D4×C11—22no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—42no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2411yescharacteristic
145C11×Q16—48no—
146C11×SD16—48no—
147C11×M16—24no—
148C11×M16—24no—
149C2×C8×C11—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—216no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—24no—
161C42×C11—24no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11C2×D414yes—
165#3487C2×C1111yescharacteristic
166C2×#536C2×C1111yescharacteristic, complemented
167C2×#456C2×C1112yescomplemented
168#3004C2×C1112yescomplemented
169#2004C2×C1114yescomplemented
170#1897C2×C1112yescomplemented
171#1886C2×C1112yescomplemented
172#1785C2×C1111yescharacteristic, complemented
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—44no—
181C23×C11#12012yes—
182C23×C11C22×D411yescharacteristic
183Q8×C11—28no—
184Q8×C11—28no—
185Q8×C11—24no—
186Q8×C11—48no—
187Q8×C11—44no—
188Q8×C11—44no—
189D4×C11—24no—
190D4×C11—48no—
191D4×C11—44no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—44no—
195D4×C11—84no—
196D4×C11—88no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—28no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—48no—
207C2×C4×C11—48no—
208C2×C4×C11—44no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11#12014yes—
214C2×C4×C11#12012yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C22×D412yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C8×C11—44no—
219C2×2−1+4C22×C1111yescharacteristic
220C22×#41C22×C1111yescharacteristic
221C23×Q8C22×C1111yescharacteristic
222C2×#137C22×C1114yes—
223#550—24no—
224#548—24no—
225#536—28no—
226#535—22no—
227#535C22×C1112yes—
228C2×C4⋊Q8C22×C1112yes—
229C2×#124C22×C1112yes—
230#525—22no—
231#525C22×C1112yes—
232C2×#123—22no—
233C2×C22⋊Q8—22no—
234#519C22×C1111yescharacteristic
235C2×#117C22×C1111yescharacteristic
236#456—28no—
237#451—24no—
238#448—24no—
239C2×#104C22×C1114yes—
240#419C22×C1114yes—
241C2×#101C22×C1112yes—
242C2×#100C22×C1112yes—
243#407C22×C1112yes—
244#339C22×C1114yes—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—24no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—44no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11—82no—
256C22×C11C2×#12011yescharacteristic
257C22×C11C2×#12011yescharacteristic
258C22×C11#53411yescharacteristic
259C4×C11—22no—
260C4×C11—24no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—44no—
264C4×C11—44no—
265C4×C11D4214yes—
2662−1+4—24no—
2672−1+4—42no—
268C2×#41—24no—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—24no—
272C2×#41—42no—
273C2×#41C23×C1112yes—
274C22×Q8—24no—
275C22×Q8—22no—
276C22×Q8—21no—
277C22×Q8—24no—
278C22×Q8—42no—
279C22×Q8C23×C1112yes—
280C22×Q8C23×C1111yescharacteristic
281C22×D4D4×C1112yes—
282C22×D4C23×C1111yescharacteristic
283C23×C4—21no—
284C23×C4D4×C1112yes—
285C23×C4C23×C1111yescharacteristic
286#137—28no—
287#137—44no—
288C2×Q16—24no—
289C2×SD16—24no—
290C2×M16C23×C1114yes—
291C4⋊Q8—24no—
292C4⋊Q8D4×C1118yescomplemented
293#127—24no—
294#127—22no—
295#124—24no—
296#124—24no—
297#124—22no—
298#124—24no—
299#123—216no—
300#123—22no—
301C22⋊Q8—216no—
302C22⋊Q8—24no—
303C22⋊Q8D4×C1114yes—
304#121—24no—
305#121—28no—
306#121—24no—
307#121D4×C1114yes—
308#120—24no—
309#120—22no—
310C4×Q8—24no—
311C4×D4—28no—
312C4×D4—24no—
313#117—22no—
314#117—24no—
315#117C23×C1112yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—24no—
320C2×C42C23×C1112yes—
321#104—28no—
322#103—28no—
323#101—24no—
324#100—42no—
325C22⋊C8—24no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11—42no—
329C2×C11—82no—
330C2×C11—82no—
331C2×C11#240311yescharacteristic
332C2×C11#302212yes—
333C24C2×D4×C1112yes—
334C24C2×D4×C1111yescharacteristic
335#41—24no—
336#41—24no—
337#41—416no—
338#41—44no—
339#41—48no—
340#41—44no—
341C2×Q8—24no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—24no—
347C2×Q8—24no—
348C2×Q8—416no—
349C2×Q8—42no—
350C2×Q8—48no—
351C2×Q8—42no—
352C2×Q8C2×D4×C1112yes—
353C2×Q8C2×D4×C1114yes—
354C2×Q8C2×D4×C1114yes—
355C2×D4—22no—
356C2×D4—24no—
357C2×D4—22no—
358C2×D4—28no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4C2×D4×C1112yes—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1114yes—
381C22×C4C24×C1111yescharacteristic
382Q16—48no—
383SD16—48no—
384M16—24no—
385M16—24no—
386C2×C8—24no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—216no—
390C4⋊C4—24no—
391C4⋊C4C2×D4×C1114yes—
392C22⋊C4—24no—
393C22⋊C4—216no—
394C22⋊C4—28no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—24no—
398C42—24no—
399C42—22no—
400C42—22no—
401C42C2×D4×C1114yes—
402C11#2391611yescharacteristic, direct product factor, Sylow
403C23—21no—
404C23—21no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—42no—
410C23—44no—
411C23C11×#12012yes—
412C23C22×D4×C1111yescharacteristic
413Q8—28no—
414Q8—28no—
415Q8—24no—
416Q8—48no—
417Q8—44no—
418Q8—44no—
419D4—24no—
420D4—48no—
421D4—44no—
422D4—42no—
423D4—42no—
424D4—44no—
425D4—84no—
426D4—88no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4C11×#12012yes—
444C2×C4C11×#12014yes—
445C2×C4C22×D4×C1112yes—
446C2×C4C22×D4×C1112yes—
447C2×C4C11×H(5,𝔽2)12yes—
448C8—44no—
449C22—22no—
450C22—22no—
451C22—24no—
452C22—42no—
453C22—42no—
454C22—44no—
455C22—42no—
456C22—42no—
457C22—44no—
458C22—44no—
459C22—82no—
460C22C2×C11×#12011yescharacteristic
461C22C2×C11×#12011yescharacteristic
462C22C11×#53411yescharacteristic
463C4—22no—
464C4—24no—
465C4—44no—
466C4—42no—
467C4—44no—
468C4—44no—
469C4D42×C1114yes—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—82no—
474C2—82no—
475C2C11×#240311yescharacteristic
476C2C11×#302212yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3487C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#536C2semidirect
3. C2×C11×#456C2semidirect
4. C11×#3004C2semidirect
5. C11×#2004C2semidirect
6. C11×#1897C2semidirect
7. C11×#1886C2semidirect
8. C11×#1785C2semidirect
61. C11×C4⋊Q8D4semidirect
95. #23916C11direct (N × H)
166. C2×#536C2×C11semidirect
167. C2×#456C2×C11semidirect
168. #3004C2×C11semidirect
169. #2004C2×C11semidirect
170. #1897C2×C11semidirect
171. #1886C2×C11semidirect
172. #1785C2×C11semidirect
292. C4⋊Q8D4×C11semidirect
402. C11#23916direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#34872
C2×C11×#5362
C2×C11×#4562
C11×#30042
C11×#20042
C11×#18972
C11×#18862
C11×#17852
#2391611